Calculus

Consider the function

f (x) = 2x^3 - 3x^2 - 72x + 7

Find and classify the critical points. Identify the intervals of increase and decrease, and state the intervals of concavity.

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asked by Liz
  1. f(x) = 2x^3 - 3x^2 - 72x + 7
    f'(x) = 6x^2 - 6x - 72 = 6(x^2-x-12)
    f"(x) = 12x-6 = 6(2x-1)

    f'=0 at x= -3 and 4
    f"=0 at x = 1/2

    Now it's easy to answer the questions.
    f is increasing where f' > 0
    f is concave up where f" > 0
    no asymptotes, so critical points where f' = 0

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    posted by Steve

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